Data-driven methods for denoising and analysis of functional magnetic resonance imaging time-series

In the last decade or so, functional magnetic resonance imaging (fMRI) has emerged as a standard tool for mapping activation patterns in the human brain. It is a highly interdisciplinary field involving neuroscientists, clinicians, physicists, mathematicians, and engineers. The experiments performed by the neuroscientists generate multitude of data which are subsequently analyzed using various analysis techniques. However, data obtained from the magnetic resonance (MR) scanners are confounded by a number of artifacts that are needed to be accounted for prior to the analysis of the data. These artifacts arise due to a variety of reasons at different stages of data acquisition and their sources vary from problems with the MR scanners to non-task related signals due to heart-beats, breathing, and other functional activities. This is the reason that on one hand, physicists and engineers have been trying to improve the performance of the MR scanners, and on the other hand mathematicians and engineers are coming up with new solutions to reduce various artifacts and to analyze fMRI data. The sequential combination of preprocessing steps applied to fMRI data, following data acquisition and including data analysis is referred to as the fMRI data-processing pipeline. Typical preprocessing steps include spatial registration of raw images to correct for small head motions, temporal interpolation to compensate for the fact that different slices are acquired at different times, filtering to enhance the SNR, and often, spatial normalization or transformation to a common stereotactic space to facilitate group analyses and neuroanatomical labeling This thesis focuses on the last two stages of the processing pipeline, denoising and analysis.Doctor of Philosoph